Josephson effects and textural dynamics in superfluid helium three

Abstract

As liquid helium three is cooled to temperatures below 1 mK, it becomes a superfluid. In this state it is able to support dissipationless mass supercurrents. Analogously to what happens for superconducting metals, when two volumes of the superfluid are brought into contact through a "weak link", phenomena known as Josephson effects arise. These are associated with supercurrents which depend periodically on the difference between the quantum-mechanical phases of the superfluid order parameters. However, the order parameter in helium three is far more complicated than that in conventional superconductors, and this gives rise to new features in the physics of weak links.

In this thesis we present theoretical and numerical considerations of the Josephson effects and dissipative currents in weak links of superfluid helium three, in particular its B phase. We use our results to analyze recent experiments.

In the case of small point contacts, we calculate the equilibrium current-phase relations, as well as the dissipative currents due to multiple Andreev reflections when the contact is biased by a pressure head. These calculations are made using quasiclassical theory. We take self-consistently into account the effects of microscopically rough surfaces on the order parameter, which is important for obtaining quantitatively correct results. For apertures whose sizes are on the order of the temperature-dependent coherence length, we compute current-phase relations using Ginzburg-Landau theory. In this case we also consider weak links involving the superfluid A phase. Using a hydrodynamical approach to the B phase, we also consider large arrays of apertures, where we introduce the new concept of "anisotextural" Josephson effect. This effect depends crucially on the presence of the spin-orbit degrees of freedom in the order parameter, and is not possible in conventional superconductors. We use this concept to interpret experiments made with array-type weak links, where so-called "pi-states" and unexpected dissipation effects were found.